This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to the field of characterization of seismic attributes. Specifically, the invention is a method for the characterization of dip, curvature, moundness or rugosity of gridded surfaces for the quantitative estimation of reservoir facies and reservoir properties.
In many geologic basins the detailed identification of faults, folds, and the degree of moundness or rugosity of a surface can be extremely useful in seismic reservoir characterization and in the development of reservoir models for fluid flow simulations. For example, faults, folds, and fractures may profoundly affect reservoir characteristics such as the producibility of oil and gas wells. Small fault planes can be resolved by seismic 3-D surveys of reasonable quality. It is well known that the folding of strata may result in the development of fractures and faults on a variety of scales. Mounding may result as differential compaction of sediments with different concentrations of sands and shales. Mounding may also highlight locations of reef structures.
One of the biggest problems when dealing with fractured or mounded reservoirs is the recognition of the most typical scale at which these features occur. The imaging of the top of a reservoir at some typical or dominant scale should bring out the most interesting geometric, topographic, or morphological character of the surface. This would provide separation of the small-scale random fluctuations from the coherent portion of the signal. In seismic acquisition, the former could be processing or interpretation noise, while the latter could be the geologic footprint
A common measure of fault-related and fold-related deformation is to calculate the structural dip, namely, the magnitude of the gradient of the depth of an interpreted seismic horizon. Another common measure of fold-related deformation is structural curvature, which is derived from the second spatial derivatives of a depth surface. Curvature can also be used to measure the moundness or rugosity of a surface. The rugosity of a surface may be an indication of stratigraphic facies (e.g. channel""s levees) rather than of structural control. Dip and curvature can be defined as geometric multi-trace attributes because their definitions require the availability of depth measurements at multiple trace locations and because they truly characterize the geometric characteristics of a surface. Dip and curvature maps define areas of steep slope and of significant bending.
The calculations of multi-trace attributes are usually performed at the highest spatial resolution afforded by the data. Unfortunately, the pervasive presence of distortions in the seismic data (local noise, and its effects on seismic interpretation) can affect the detection of features by failing to identify larger trends. Smoothing and re-gridding of the initial surface are commonly employed to provide attribute maps at different spatial scales. These maps are then used to analyze the regional and local structural and stratigraphic facies. However, the smoothing and re-gridding are often applied subjectively and with a corresponding loss of resolution.
Current technology relies heavily on 3-D seismic data for delineation of faults and depositional environments. However, the process usually involves gridding of the surface output from the 3-D data and the filtering out of its high-resolution component. Current commercial implementations of these types of geometric attributes require smoothing or re-gridding of the data and specifically several intermediate and often subjective manipulations of the data.
Most vendor software packages (e.g., ARC/Info, ZMap) calculate geometric attributes using first and second derivatives along two orthogonal directions, and then sum up their contributions to arrive to an approximate value of Dip and Curvature. The calculations of such geometric attributes at greater spatial scales require the re-gridding of the surface to a coarser grid (bigger cell size). Invoking several smoothing passes usually minimizes noise in the map appearance. These vendor applications are more suited for calculation of such attributes on conventional 2-D seismic data where the more sparse and irregular data must be gridded for analysis and the coarseness of the 2-D seismic coverage lends itself to such gridding. Maps constructed from 3-D data using these vendor applications often need to be gridded and smoothed significantly in order to see geological features. Much detail and resolution are lost. Gridding at small bin size, close to the actual trace spacing, results in surface attributes that are often overwhelmed by noise and offer a very narrow range of values. Geometric attribute maps appear meaningless, often with no apparent discernible pattern. Manipulations of the color scale do not show any improvement.
Stewart S. A. and Podolski R. (1998), xe2x80x9cCurvature analysis of gridded geologic surfacesxe2x80x9d, Coward M. P., Daltaban T. S. and Johnson H. (eds.), Structural Geology in Reservoir Characterization, Geological Society of London, Special Publications, 127, 133-147, discuss how dip and grid lattice orientation affect the resulting estimates of the true surface curvature, thus stressing the approximations provided by common vendor packages. However, they fail to recognize the interdependencies of the various measures of curvature as they focus on the determination of the principal curvatures. Their main recommendations involve careful gridding, smoothing (despiking), and calculations at many offsets and at multiple orientations. Such steps are not necessary, as knowledge of the Gaussian and Average curvatures is sufficient to determine the principal curvatures. Detailed time consuming calculations of curvature along multiple orientations are not necessary.
Lisle R. J. (1994), xe2x80x9cDetection of zones of abnormal strains in structures using Gaussian Curvature Analysisxe2x80x9d, AAPG Bulletin, 78,1811-1819, follows a similar procedure, as indicated by its selection of the neighboring points for estimating KG. Specifically, it uses smoothing and contouring before the calculation of curvature. The method does not yield the principal curvatures and the corresponding principal axes. There is also no mention on how to deal with noisy data. The implicit assumption is that the smoothing and contouring takes care of such situations.
Generally, the published papers describing the geological applications of curvature give an incomplete treatment of the interdependencies of its various measures. They mostly focus on Gaussian curvature or discuss the azimuthal dependency of the principal curvatures. One issue that is often avoided is the recognition of the difficulty of applying the mathematical concepts when dealing with gridded, noisy data. This is treated in Padgett M. J. and Nester D. C, (1991), xe2x80x9cFracture evaluation of Block P-0315, Point Arguello Field, offshore California, using core, outcrop, seismic data and curved space analysisxe2x80x9d, 1st AAPG SPE et al Conference, Houston, Tex., 242-268; and Luthy S. T. and Grover G. A., (1995), xe2x80x9cThree-dimensional geologic modeling of a fractured reservoir, Saudi Arabiaxe2x80x9d, 9th SPE Middle East Oil Show, Bahrain, 419-430. The concept of the scale of the features under analysis is also often avoided, thus failing to recognize the existence of an optimal, data-determined scale giving the best-focused images.
Stewart and Podolski (1998) give the most complete treatment of the problem to date. They discuss 1) a moving window method, 2) the scale dependency of the results, 3) argue for multiple curvature extractions, 4) understand the effect of the inclusion of dip on the curvature calculations. However, they (1) focus on principal curvatures and normal curvature, (2) fail to recognize the importance of larger window sizes as a noise-reduction procedure, and (3) are swayed by the effect of aliasing when calculating curvatures along various orientations when such an approach is not necessary. Additionally, their paper describes critical issues in geometric attribute analysis without recommending any specific algorithm for calculating stable, robust geometric attributes as the present invention does.
The understanding of the solution of the problem came from theoretical and numerical analysis of synthetic surfaces, of various shapes and orientation, over which small-scale noise was added. None of the currently available vendor packages appears to be capable of providing all the various measures of curvature described above or the corresponding azimuths or principal axes with the detailed resolution achieved by the present invention.
Thus, there exists a need for an efficient method to apply such mathematical operations to attribute maps for quantitative seismic facies analysis or to stratigraphic horizons for the identification of moundness or rugosity of surfaces.
The present invention is a method for calculating a multi-trace geometric attribute of a regularly gridded surface at multiple scales. First, a window size is selected. Next, a set of the grid points is defined defining grid cells of the selected window size. Next, the geometric attribute is calculated using the traces at the set of the grid points. Next, the above selecting and calculating steps are repeated for sets of the grid points defining grid cells of different window sizes. Finally, the window size is determined whose calculations best represent the geometric attribute.